The Poles have an outspoken ambivalence about their Soviet big brothers even at the best of times, and it was not the best of times when the Moscow rock band Zvuki Mu played Warsaw in May. Demonstrators were marching in the streets, and students had shut down the university in sympathy with striking miners and shipyard workers. As Zvuki Mu took the stage, recalls Sasha Lipninsky, the band's bass player, there were cries of "Soviets go home!" from the restless crowd of Polish punks in black leather and spiked hair.

Then the spotlight settled on the lead singer, Pyotr Mamonov. Mr. Mamonov is one of the most captivating showmen in the Soviet Union. When he sings, his entire elastic physique contorts into compositions of anguish and confusion and ecstasy, giving an absurd body English to the lyrics he describes as "Russian folk hallucinations."

Before long, the catcalls died down, and the Polish punks were turning to each other as if to ask: What on earth is this?

This is Soviet rock, and it is finally making its long-promised bid for the attention of the outside world.

Soviet rock has matured dramatically in the last year, as was evident when the Moscow Rock Laboratory, an officially sanctioned club that promotes musicians who do not belong to state concert organisations, held its annual summer festival in June. Six bands played on the opening evening, and all of them were at least entertaining. The instrumentals have become sharper, the lyrics more biting, the staging more professional. The show stealer was a young, psychedelic funk band called Nuance, with a flashy lead guitarist who unleashed astonishing riffs while stretched out face-down on the stage.

Until this year, however, Soviet bands had little chance to become known to listeners outside the country. A 1986 sampler album of underground rock bands, Red Wave, compiled from bootlegged tapes, was moderately successful in The United States. MTV, the music-video cable service, broadcast a special on Soviet rock a year ago. But only officially sanctioned - usually bland - groups were given visas to perform abroad.

One important breakthrough came this summer when Soviet authorities let Boris Grebenshchikov, a talented folk-rock balladeer who heads the Leningrad group Aquarium, travel to Los Angeles to record an album for CBS. The record is due out in January, and the company is deploying a promotional campaign designed to make him the first crossover star in Soviet rock.

Zvuki Mu has come under the patronage of Brian Eno, who produced U2's best-selling album The Joshua Tree and has been one of rock's most influential purveyors of the eclectic and original. A record may be released in The United States early next year.

The realists among Soviet rockers know that their music is probably fated to be a novelty item in the West. At best they hope for a modest audience in Europe and a cult following in The United States. But after two decades of enforced isolation, Soviet musicians are revelling in their first taste of Western exposure, and their liberation promises some unexpected pleasures for Western listeners.

European audiences are now seeing concerts by the most interesting Soviet bands, who a year ago were not allowed to travel abroad. Zvuki Mu recently played in Rome along with three other interesting groups: a jazzy swing band called Bravo, a satirical Lithuanian rhythm and blues band called Antis, and Televisor, a defiant Leningrad group known (and frequently banned at home) for such anti-authoritarian anthems as Get Out Of Control and My Father Is A Fascist.

Hamburg was treated to a concert this fall by Avia, a brassy band with a cleverly choreographed stage show that is a hilarious lampoon of Soviet revolutionary agit-prop. Managers of some American clubs are now talking about importing some of these groups for United States audiences. Although non-controversial pop singers such as Alla Pugachova (who might be considered the Soviet Union's answer to Liza Minnelli) have had the opportunity to tour The United States - Russia's underground rock bands have not yet performed in America.

The Soviet Union has had a lively rock subculture since the 1960s - there is plenty of stimulus for an inherently anti-authority musical form - but its growth has been stunted by a disapproving state.

The record system here consists of one state-run label, Melodiya, with limited recording studios and pressing facilities and a penchant for the most conservative music. The more interesting rock music comes out on tapes, which are duplicated - mostly on simple cassette-to-cassette recorders - and circulated hand-to-hand. When Aquarium cut their first Melodiya record, the state record monopoly borrowed the group's bootleg tapes as the basis for the recording. A few individual musicians now have assembled their own recording studios with multi-track taping equipment, not state of the art but acceptable, but the performers' dream of independent record labels is still unrealised. Even in the era of glasnost, many consider rock decadent and subversive.

Last year, in a Moscow newspaper, one official commentator memorably described rock music as "ideological AIDS." Recently a professor at a Leningrad medical school wrote in a local newspaper that exposure to rock causes physical debilitation, psychological breakdown, drug addiction and homosexuality.

Despite such critics, in the last two years rock has percolated up from the underground and found official tolerance, if not affection. Private entrepreneurs and local branches of the Communist Youth League now vie with Gosconcert, the state concert agency, to organize concerts for amateur bands, opening up new venues, bringing better pay and often forgoing the traditional pre-concert censorship of lyrics.

The hip, late-night TV show Vzglyad ("View") has broadcast video clips - often made by professional film makers who are friendly with the musicians - from some of the most daring Soviet rock groups. Prime time, however, is still largely off-limits to anything more adventuresome than Europop festivals and wholesome Soviet disco.

Gradually it seems to have dawned on Soviet authorities that letting Televisor sing My Father Is A Fascist in Hamburg would probably not bring Communism to its knees, might be a good advertisement for glasnost and could even bring in some foreign currency. The question remains, does the West want Soviet rock? There are good reasons to doubt it.

For one thing, observes Artemy Troitsky, the leading Soviet rock critic, Russian groups still lack the technical proficiency and stage presence to impress an American audience. "Soviet bands, no matter how interesting and original, are still very much underproduced by Western pop music standards," said Mr. Troitsky, whose book on Russian rock, Back In The USSR, was published in England last year. "Aside from the problems of expertise and equipment, they do not know how to behave."

Mr. Troitsky offers as evidence the top Soviet heavy-metal band, Kruiz, who recently played in Sweden: "They played very well, good drummer and good guitars, but their stage number is ridiculous to heavy-metal fans. After a song, they smile and bow like in a Eurovision song contest."

A bigger handicap is that Americans, in particular, have never been very receptive to performers working in foreign languages, and the best Soviet rock musicians tend to have literary aspirations. Soviet rockers see themselves as poets rather than musical innovators - so what is most original in their work may be least accessible to a Westerner.

Boris Grebenshchikov has set out to succeed on Western terms. He wrote nine of the ten songs on his CBS album in English, and the production by David A. Stewart of The Eurythmics is layered with electronic flourishes unavailable in Leningrad. There are background vocals on a few cuts by Annie Lennox of The Eurythmics and Chrissie Hynde of The Pretenders. The promotion campaign is to include a feature-length film about the singer, who is an articulate, photogenic and charming subject. Mr. Grebenshchikov will have his name cosmetically altered for Western consumption - to Grebenshikov.

In his own country he has a reputation as a Russian Bob Dylan whose mix of Russian Orthodox religious mysticism, social commentary and romanticism touch something familiar in the Russian soul - something Russians like to believe is beyond the understanding of non-Russians.

Listeners curious about this ineffable Russianness will have to listen hard to find it in Mr. Grebenshchikov's forthcoming American album. The record contains several tributes to the Beatles - the greatest influence on early Soviet rock - a disco number, and a couple of tunes in the English-Irish folk tradition. The one song in Russian is an unadorned acoustical ballad by the late Russian poet, Aleksandr Vertinsky. In general, Mr. Grebenshchikov's sound is submerged much of the time in Mr. Stewart's synthesizers, and his writing, which seems so achingly poetic in Russian, is often a bit trite in English.

"If Bob Dylan were not an American, he would never be so popular in America," said Sasha Lipninsky, Zvuki Mu's bass player. "Boris, I think, is too Russian, too sentimental, to be a very big success in America. But he also has the talent to adapt, so we'll see."

Zvuki Mu hopes to find its Western audience by clinging to its Russian eccentricities which, aside from Pyotr Mamonov's stage presence, include lyrics that range from grotesque alcoholic ravings to alienated soliloquies about love. In one song Mr. Mamonov compares his lover to a fly, "a source of infection." Zvuki Mu means literally "the sounds of mu." It is meant as a reference to the lowing of cows, and is also a satirical play on The Sound Of Music, which is popular in the Soviet Union.

Mr. Eno's wife and manager, Anthea Norman-Taylor, said that when the producer comes to Moscow in November to record tracks for a possible album, the group will sing their own material, in Russian. Mr. Eno, she said, believes the group's appeal is in "their spirit, and an interesting poetical sense, an onomatopoeic quality."

Mr. Mamonov's deep voice does have a raw, hysterical edge that transcends lyrics. Zvuki Mu's music is spare and simple, built on familiar guitar and keyboard riffs borrowed from funk, blues, reggae and the odd waltz. But Zvuki Mu is best in performance, and it is hard to imagine that the band will find its way into America's Top 40.

Mr. Lipninsky said no Soviet band should expect to be more than a curiosity in the West, a novelty tied to the policy of social change Mr. Gorbachev calls perestroika.

"The interest of the West will last for a year, maybe two years," he said. "I am not an optimist about our perestroika, and when the West realizes that all these changes have slowed down, they will lose interest in Soviet rock."

But even a minor success in the West will help Soviet rock musicians in their perennial war with the Soviet cultural establishment, where any evidence of Western approval carries enormous cachet. A band that has performed or recorded in the West - has competed on the world level, as Mr. Gorbachev likes to say, presumably with machine tools more on his mind than Zvuki Mu - has the status to get on television, to get scarce musical equipment, to get a concert hall or to cut a record.

"Soviet rock going to the West is probably not very important for the West," Mr. Lipninsky said. "But it is very important for Soviet rock."